A Restricted Four-body Problem for the Figure-eight Choreography

In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the figure-eight choreography, and explore some symmetric periodic orbits of this system which turns out to be nonautonomous. We use reversing symmetries to study both theoretically and numerically a certain type of symmetric periodic orbits of this system. The symmetric periodic orbits (initial conditions) were computed by solving some boundary-value problems.